NAME:_______________________
December 15, 2016
APPLIED 40S - CHAPTER 3
Answer all questions on this test paper. As much as possible, show your work, as part marks cannot be awarded if the
answer is wrong and no work is shown. Please allot your time to each question on the basis of marks.State all decimal
answers correct to two decimal places!
1. Students were surveyed about the technology they own.
A owns a notebook computer
B owns a tablet computer
Which of the following statements is true?
A. nA21
B. nBˊ36
C. nA ∩ B9
D. nA U B76
2. Given the following sets:
U=1, 3, 5, 7, 9, 13, 17, 21}
A = {1, 9, 13, 21}
B = {1, 7, 9, 17, 21}
a) Illustrate these sets using a Venn diagram.
(2)
b) Determine A′U B.
(1)
c) Create a set C with 3 elements, where C ⊂B.
(1)
(1)
3. Represent the following sets in a Venn diagram:
U  Argentina, Bolivia, Brazil, Chile, Columbia, Ecuador, Paraguay, Peru, Uruguay, Venzuela
A  countries that start with a vowel
B  countries that end with a vowel (including y)
C  countries that start with a consonant
(4)
For the above Venn diagram determine:
a) n  A  B 
b) B  C
c) n  A  C 
(1)
(1)
(1)
d) B '
e) true or false: n  A  n  B   n  C   n U 
(1)
(1)
f) name two sets that are disjoint
(1)
4. A class of 28 students was surveyed to discover the type of music to which they listen.
 12 students said they listen to country
 18 students said they listen to pop
 2 students said they listen to neither country nor pop
Determine the number of students who listen only to pop. Show your work.
(2)
5. There are 160 Grade 12 students attending a high school.
This semester, the science teacher noted that there are
 30 students in Biology
 54 students in Chemistry
 43 students in Physics
 11 students in both Biology and Physics
 8 students in both Biology and Chemistry
 9 students in both Chemistry and Physics
 3 students taking all three courses
a) Use a Venn diagram to represent this situation.
(3)
b) How many students are taking Biology or Chemistry?
(1)
c) how many people take only Physics?
(1)
d) how many people take no sciences?
(1)
6. For the conditional statement “If you are in Vocal Jazz, then you are in School Chorus” write the:
a) converse:
(3)
b) inverse:
c) contrapositive:
7. If the conditional statement is true, which of the other 3 forms MUST also be true?
(1)
8. a) For a biconditional statement, which forms of the conditional statement are true?
(1)
b) write the following statement as an IFF statement.
“If a number is even, then it is divisible by two”
(1)
9. For the following Venn diagrams, label by shading:
a) A  B
A
B
(1)
b) A \ B
A
B
(1)
c) A '
A
B
(1)
d) A  B
A
(1)
B
16. a) Use the numbers 1, 2, 3, 4, 5, 6 only once to complete the chart.
(2 marks)
b) What were the first two numbers you obtained?
Explain the strategy you used to obtain these numbers.
(1 mark)
/36
Bonus: If a multiple choice quiz has 4 questions, each with 3 possible answers, how many
possible answer keys are there?